EXPERIMENTAL DETERMINATION OF   THRESHOLD OF RIVER MEANDERING AND BRAIDING

Habibi, M. and Haghiabi, A. H.

Soil Conservation and Watershed Managment Research Center,

P.O.Box 13445-1136, Tehran, Iran

Abestract: A series of experiments was performed in a laboratory flume to determine the threshold of meandering and braiding of river patterns. For the purpose, of modeling, an alluvial reach of Ghezel Ozan (a meandering river in central north of Iran) was selected and using reasonable values of geometric, hydraulic and bed material properties of this river, a physical model with horizontal scale of 1:400 and vertical scale of 1:40 was constructed.

After performing several laboratory tests, it was found that discharge and slope were closely related to the threshold values of channel patterns. Also based on regression analysis of experimental results a number of analytical relationships were obtained for determining the threshold of meandering and braiding patterns. The proposed relationships are between the channel longitudinal slope and discharge and between the “Non-dimensional Unit Stream Power (NUSP) and Shields parameter”. The later is a new and interesting relationship in river morphology. Several diagrams were made to show that under what initial conditions the meandering and braiding patterns are established.

The laboratory observations of this research have indicated that at very low NUSP, the channel remains straight, but at NUSP of 5.5 to 6.5 a meandering channel is formed and as NUSP increases to 12-22 a braided channel is formed. 

Keywords: river morphology, meandering, braided, physical modeling, channel pattern

1    INTRODUCTION

River channel patterns are mainly classified to straight, meandering and braided. Lane(1975), Leopold and Wolman(1957), Henderson(1963), Ackers and Charlton(1970) and Osterkamp(1978) suggested some equations between slope and discharge for determining the threshold of meandering and braiding patterns [1 and 2]. Schumm and Khan(1972) based on slope and sediment load, Parker(1976) based on depth/width ratio and slope/Froude Number ratio, Brotherton(1979) based on erodibility and transportability of bank particles suggested some diagrams for predicting the river pattern [2]. Silva(1991) based on depth/particles size and width/depth ratios distinguished meandering and braiding patterns [6]. Fredsoe(1978) based on Shields parameter and width/depth ratio, Blondeaux and Seminara(1986) based on particle Froude Number and depth/width ratio, Kuroki and Kishi(1985) based on Shields parameter, slope and width/depth ratio suggested some diagrams for river planfrom classification (Straight, Meandering and Braided) [3].Yang(1976), Ferguson(1984), Carson(1984), Schumm and Khan (1972) and Yalin(1992) believe that channel pattern change is associated to stream power [3].

Herein, some laboratory attempts were made to determine the threshold of meandering and braiding based on slope, discharge, Sheilds parameter and non-dimensional unit stream power.

2    SIMULATION

In order to design the laboratory model the characteristics of a meander loop of Ghezel Ozan River were selected as follows:

River mean width = 16 m

Manning coefficient = 0.020

Channel slope = 0.0007

Median size of bed material, D₅₀ = 13.4 mm

Meander bend radius = 800 m

Width of meander belt = 400 m

River discharge with a return period of 5 years, Q₅ = 343.4 m³/sec

River discharge with a return period of 10 years, Q₁₀ = 535.14 m³/sec

River discharge with a return period of 25 years, Q₂₅ = 798 m³/sec

River discharge with a return period of 50 years, Q₅₀ = 1001.45 m³/sec

River discharge with a return period of 100 years, Q₁₀₀ = 2414.7 m³/sec

Considering the laboratory limitations and flow conditions and using the Froude law of similarity, a distorted model was designed with horizontal and vertical scales of 1:400 and 1:40 respectively. Then the scales of slope, discharge and bed material were obtained as:

Slope scale = =

Discharge scale = =

Particle size scale =

3    EXPERIMENTAL PROCEDURE

3.1    Laboratory equipment

The experiments were performed in a re-circulating flume 14m long, 1.5m wide and 0.8 m deep with fiberglass walls along its length. A steel bridge was mounted on the flume walls and was able to move across the width and along the length of the flume. The bridge was equipped with a point gage. These facilities were used to establish a co-ordinate system, for measuring the channel bed morphology (Fig. 1).

In each experimental run, water entered the upper end of the flume through entrance baffles and after becoming calm, it passed through the model and discharged into a tail box. An axial pump was then used for circulating the water. The discharge was measured with a triangular weir at downstream end of the flume.

3.2    Procedure of experiments

Before each test, the flume was filled to a depth of 25 cm with sand having a median size of 3mm. The sand surface in the flume was smootened, and the desired channel was then excavated along the center-line of the flume bed (Fig.2). The initial channel was about 20 cm wide and 10 cm deep. In each test the channel bed was carefully graded to the desired slope, and then sand was removed in order to form the channel banks with uniform height. The channel slope along the axis of the flume is used for further analysis throughout this paper.

In each run, water entered into the channel using the re-circulating pumps, and discharge was gradually increased to the desired amount. A number of 31 tests were performed with discharge ranged from 1 to 8 lit/s and the slopes of 0.002, 0.003, 0.007, 0.014, 0.018, 0.020 and 0.022. [see Figs. 3, 4, 5 and 6].

At the beginning and end of each experimental run the longitudinal profile and a series of cross sections were measured, and a topographic map of the channel was prepared. This made possible the calculation of channel hydraulic radius, width/depth ratio and so on. Also, based on these measurements, the average velocity, bed shear stress, Froude number, Shields parameter and non-dimensional unit stream power were calculated.

4    EXPERIMENTAL OBSERVATIONS

Displacement of thalweg line: At entrance to the channel bend, the thalweg line is located adjacent to the convex bank, but after passing the bend it immediately dislocates to the concave bank. At bend apex, thalweg is deep and narrow and erosion along the concave bank is active and the area between concave bank and thalweg is exposed to mass falling of bank material.

Armoring phenomenon: With time passing and channel pattern developing, the armoring phenomenon happens, the longitudinal slope decreases, the finer particles move downstream and flow leaves out the coarser bed materials; so, the coarser sediments are found in the lower section of point bars and the finer sediments are in the upper section.

Channel pattern development: Using laboratory measurements and calculating the values of non-dimensional unit stream power (NUSP) and Shields parameter (q) for each experimental run, Fig.7 has been obtained to show the relationships between NUSP and q in relation to channel pattern establishment. Based on this Fig., at a very low NUSP (NUSP = QS/DÖgD⁵), the channel remains straight, but at a NUSP of 5.5 to 6.5 a meandering channel forms (Meandering threshold); at this condition, Shields parameter q (q = ) is 0.01 to 0.03 and at a NUSP of 12 to 22 a braided channel forms (Braiding threshold) where at this condition, Shields parameter is 0.09 to 0.1. In the other words, initial channel with above-mentioned NUSP and shields parameter values is finally capable to establish a meandering or braided pattern.

With increasing NUSP, the channel pattern is altered from straight to meandering and braided. The above-mentioned matter is true in relation to Shields parameter too.

After establishment of regime channel, at all runs, the Shields parameter (q) becomes constant with a value very close to 0.056, which is the critical Shields parameter. Since the constant value is equal to or slightly less than critical Shields parameter, channel pattern development stops and no further development happens unless the hydraulic and sediment variables that affecting Shields parameter are changed in a way that Shields parameter becomes greater that its critical value.

After regime channel establishment, the stream power decreases because the river has dissipated its excess power with bed and bank erosion. In that condition stream power per unit length, i.e. “rgQS” minimizes and since r and g are constant, with a constant value of Q, S minimizes.

5    Results

Based on experimental observations, laboratory measurements and established channel patterns, the following relationships were obtained between slope and discharge in relation to channel pattern development: 

The above-mentioned relationships are comparable with those obtained by Lane (1957). Lane’s relationships are:

S = 0.004 Q^-0.25         for Braided Pattern

S = 0.0007 Q^-0.25              for Meandering Pattern

Based on laboratory data and established channel patterns the following relationships were obtained between NUSP and Shields parameter in relation to channel pattern.

6    RECOMMENDATION FOR FURTHER RESEARCH

(1) The effect of variation of bed and bank particle size on channel pattern development could be studied further using variable particle size.

(2) With simulating flood hydrograph, the influence of discharge oscillations on channel pattern development can be studied.

(3) Instead of D₅₀ in concerned relationships, statistical parameters of grain size distribution curve such as average particle size, standard deviation, … can be used for suggesting more reasonable relationships. 

Acknowledgements

This work was performed with financial support of Soil Conservation and Watershed Management Research Center of IRAN. The junior author performed the experiments as part of requirements for M. Sc. degree in irrigation structure engineering. The authors thank Dr. J. Mohammadvali Samani and Mr. H. R. Peirovan for their suggestions on the work.

List of symbols

D = Characteristic size of sediment

D₅₀ = Mean size of sediment

g = Acceleration due to gravity

P = Non-dimensional unit stream power (NUSP)

Q = Flow discharge

R = Hydraulic radius

r = Correlation coefficient

S = longitudinal slope of laboratory channel; slope of meander valley

M = Scale factor [the ratio of model value to prototype value]

D = (r_s- r)/r, Relative density of bed material

q = Shields parameter

r = Density of water

r_s = Density of sediment

t = Shear stress

Refrences

[1]  Chang. H. H. (1988), Fluvial processes in river engineering, John Wiley and Sons.

[2]  Knighton, D. (1982); Fluvial forms and processes, London

[3]  Przedwjski, B. et al. (1995); River training techniques: Fundamental, Design and application, Balkema, Netherlands.

[4]  River meandering (1984). Proceedings of the conference Rivers, 83, ASCE, Charles, M. E. Editor, Newyork.

[5]  Schumm. S. A., Khan. H. R. (1972); Experimental study of channel patterns S. Geol. Sco. Am., 83, June.

[6]  Yalin. M. S. (1992): River Mechanics; Pergamon press; Oxford.

Fig. 1    Established bed form and measurement facilities [Q = 5 lit/s; S = 0.02; 10 hours after beginning of test]

Fig. 2    Channel sloping and excavation in the experimental flume

Fig. 3    Channel pattern change, Q= 2 and 5 lit/s, S= 0.020

Fig. 4    Channel pattern change[Q = 2, 3, 4, 5 and 8 lit/s, upstream slope S₁ = 0.0007]

Fig. 5    Meandering pattern development [Q = 2 and 3 lit/s; S = 0.018] 

Fig. 6    Channel pattern change, Q = 2, 3, 4 and 5 lit/s, and S = 0.014

Fig. 7    Channel pattern distinguishing based on non-dimensional unit stream power    and Shields parameter